I would like to have it so the texture is linked to an empty point
Put some kind of mask into the object space of the Empty, using the bottom slot in a Texture Coordinate node:



Here, the Empty is a circle, and we're interested in the Y dimension of its object space. The Value input node labelled  'Fade' is provided to adjust the sharpness of the transition.

The character can be made the parent of the Empty, so it will work wherever the character happens to be.

To achieve a complete change of clothes, geometry and all,  the cluster of nodes determining the Factor of the mix could be made into a Node Group, and the mask made between opacity and transparency on all materials concerned. But if things got too tangled, you might consider using compositing instead.